In this review, I will introduce a need for research in the field of correlations between arithmetic skills and higher order mathematics. I will review several literary and research articles that are relevant to the topic, both in favor and contrary to my hypothesis. In the review, I will also make a suggestion for the type of research that will be done in order to identify and clarify the holes in the research already conducted.
The need for arithmetic remediation for middle and high school students is obvious to me as a high school math teacher in a rural Florida town; however, others have also argued that the computational capabilities of American students appear to be falling. “Tom Loveless of the Brookings Institute has reviewed responses to select items on the National Assessment of Educational Progress (NAEP) and concluded that performance on basic arithmetic facts declined in the 1990s” (Loveless, 2003). This data is further confirmed by taking a look at SAT scores, the largest drop in math scores in 30 years was reported by the Wall Street Journal in 2007 [ (Goldstudentcom, 2010) ]. Clearly, students need help to develop rapid, effortless, and errorless recall of basic math facts.
In today’s global economy, the need for post-secondary education and/or training has become more important than ever. By far, the largest remediation problem is in math. The number of recent high school students taking pre-college math is high – 10,970 students in 2006-07 [ (League of Education Voters, 2012) ]. Students entering college with skills below the college-readiness level must take pre-college math courses before starting on their required math sequence in college. These pre-college courses are costing students and America millions of dollars. In Florida alone, “$17.5 million was spent by community and technical college statewide in 2006-07 on remediation for recent high school graduates in two-year community and technical colleges” [ (League of Education Voters, 2012) ].
Due to the staggering facts in the drop in mathematics scores and the cost to our economy for remediating students in college, it is imperative that we find a way to improve on high school student performance. Just as automatic instructional practices in literacy activities can have significant benefits for students, similar practices may be beneficial for students who are lacking in mathematical skills. The use of arithmetic remediation with high school students may not be a cure all; however, it would be a step in the right direction.
I would like to conduct an educational study that focuses on the correlation of poor arithmetic skills, to poor performance in higher order mathematics of high school students. In specific, I would like to see how low skill levels in multiplication, division, addition, and subtraction effect student performance in algebra. It has been said that “poor recall of facts leads to difficulties executing calculation procedures and immature problem-solving strategies” (Killingberg, 2005). This has been argued in both reading and mathematical forums for some time, and I have found that a majority of students that struggle in my algebra classes cannot perform simple arithmetic, without a calculator. I believe that there is a direct correlation between the amount of time a student takes to find a simple solution to an arithmetic problem and how hard it is for that student to complete an algebraic equation. The hypothesis of this research is that the students that use too much of their working memory on simple arithmetic facts, have difficulty processing higher order mathematical skills.
What We Know
Working memory refers to a mental workspace, involved in controlling, regulating, and actively maintaining relevant information to accomplish complex cognitive tasks (e.g. mathematical processing) (Raghubar,